A317321 Multiples of 21 and odd numbers interleaved.

0, 1, 21, 3, 42, 5, 63, 7, 84, 9, 105, 11, 126, 13, 147, 15, 168, 17, 189, 19, 210, 21, 231, 23, 252, 25, 273, 27, 294, 29, 315, 31, 336, 33, 357, 35, 378, 37, 399, 39, 420, 41, 441, 43, 462, 45, 483, 47, 504, 49, 525, 51, 546, 53, 567, 55, 588, 57, 609, 59, 630, 61, 651, 63, 672, 65, 693, 67, 714, 69

Offset

0,3

Comments

Partial sums give the generalized 25-gonal numbers (A303304).

a(n) is also the length of the n-th line segment of the rectangular spiral whose vertices are the generalized 25-gonal numbers.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Formula

a(2n) = 21*n, a(2n+1) = 2*n + 1.

Multiplicative with a(2^e) = 21*2^(e-1), and a(p^e) = p^e for an odd prime p. - Amiram Eldar, Oct 14 2023

Dirichlet g.f.: zeta(s-1) * (1 + 19/2^s). - Amiram Eldar, Oct 26 2023

Mathematica

a[n_] := If[OddQ[n], n, 21*n/2]; Array[a, 70, 0] (* Amiram Eldar, Oct 14 2023 *)

Prog

(PARI) concat(0, Vec(x*(1 + 21*x + x^2) / ((1 - x)^2*(1 + x)^2) + O(x^60))) \\ Colin Barker, Jul 29 2018

Crossrefs

Cf. A008603 and A005408 interleaved.

Column 21 of A195151.

Sequences whose partial sums give the generalized k-gonal numbers: A026741 (k=5), A001477 (k=6), zero together with A080512 (k=7), A022998 (k=8), A195140 (k=9), zero together with A165998 (k=10), A195159 (k=11), A195161 (k=12), A195312 k=13), A195817 (k=14).

Cf. A303304.

Sequence in context: A035419 A218249 A040433 * A080472 A118389 A077690

Adjacent sequences: A317318 A317319 A317320 * A317322 A317323 A317324

Keyword

nonn,easy,mult

Author

Omar E. Pol, Jul 25 2018

Status

approved