Mewbourne Energy Partners 04-a 10-K 2011 FY Annual report

EXHIBIT 32.1

CERTIFICATION OF

CURTIS W. MEWBOURNE / CHIEF EXECUTIVE OFFICER

OF MEWBOURNE DEVELOPMENT CORPORATION

PURSUANT TO 18 U.S.C. § 1350

I, Curtis W. Mewbourne, Chief Executive Officer of Mewbourne Development Corporation, Managing General Partner of Mewbourne Energy Partners 04-A, L.P. (the “Registrant”), hereby certify that the accompanying report on Form 10-K, for the annual period ended December 31, 2011 and filed with the Securities and Exchange Commission on the date hereof pursuant to Section 13(a) of the Securities Exchange Act of 1934 (the “Report”) by the Registrant fully complies with the requirements of that section.

I further certify that the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Registrant.

/s/ Curtis W. Mewbourne

Name: Curtis W. Mewbourne

Date: March 30, 2012

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