A135435 - OEIS

A135435

a(n) = a(n-4) + a(n-7) with a(0), ..., a(6) = [7,0,0,0,4,0,0].

7, 0, 0, 0, 4, 0, 0, 7, 4, 0, 0, 11, 4, 0, 7, 15, 4, 0, 18, 19, 4, 7, 33, 23, 4, 25, 52, 27, 11, 58, 75, 31, 36, 110, 102, 42, 94, 185, 133, 78, 204, 287, 175, 172, 389, 420, 253, 376, 676, 595, 425, 765, 1096, 848, 801, 1441, 1691, 1273, 1566, 2537, 2539, 2074, 3007, 4228

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OFFSET

0,1

COMMENTS

Of interest because {7,11} is the earliest pair of typical primes belonging to a single hexad. Herein "pseudoprime" means sequence-specific psp. (i.e. dividing its term with rem. 0), not general number-theoretic psp. The only psp.s of concern, from the standpoint of primality testing, being those congruent to 1 or 5 (mod 6), are the six quadratics of the present zero-termed primes 5,13,17 the only relevant psp.s of this sequence? Or are there additional examples > 289?

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 1, 0, 0, 1).

FORMULA

G.f.: (7-3*x^4)/(1-x^4-x^7). - R. J. Mathar, Oct 24 2009

MATHEMATICA

LinearRecurrence[{0, 0, 0, 1, 0, 0, 1}, {7, 0, 0, 0, 4, 0, 0}, 70] (* Harvey P. Dale, Jan 20 2013 *)

PROG

(PARI) Vec((7-3*x^4)/(1-x^4-x^7) + O(x^80)) \\ Michel Marcus, Oct 14 2016

CROSSREFS

Cf. A133394.

Sequence in context: A229658 A306755 A005070 * A339442 A331748 A171917