A317323 Multiples of 23 and odd numbers interleaved.

0, 1, 23, 3, 46, 5, 69, 7, 92, 9, 115, 11, 138, 13, 161, 15, 184, 17, 207, 19, 230, 21, 253, 23, 276, 25, 299, 27, 322, 29, 345, 31, 368, 33, 391, 35, 414, 37, 437, 39, 460, 41, 483, 43, 506, 45, 529, 47, 552, 49, 575, 51, 598, 53, 621, 55, 644, 57, 667, 59, 690, 61, 713, 63, 736, 65, 759, 67, 782, 69

Offset

0,3

Comments

Partial sums give the generalized 27-gonal numbers (A316725).

a(n) is also the length of the n-th line segment of the rectangular spiral whose vertices are the generalized 27-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) = 23*n, a(2n+1) = 2*n + 1.

From Colin Barker, Jul 29 2018: (Start)

G.f.: x*(1 + 23*x + x^2) / ((1 - x)^2*(1 + x)^2).

a(n) = 2*a(n-2) - a(n-4) for n>3. (End)

Multiplicative with a(2^e) = 23*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 + 21/2^s). - Amiram Eldar, Oct 26 2023

Mathematica

With[{nn=40}, Riffle[23*Range[0, nn], Range[1, 2*nn, 2]]] (* or *) LinearRecurrence[{0, 2, 0, -1}, {0, 1, 23, 3}, 80] (* Harvey P. Dale, May 05 2019 *)

Prog

(PARI) concat(0, Vec(x*(1 + 23*x + x^2) / ((1 - x)^2*(1 + x)^2) + O(x^60))) \\ Colin Barker, Jul 29 2018

Crossrefs

Cf. A008605 and A005408 interleaved.

Column 23 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. A316725.

Sequence in context: A040519 A040520 A271473 * A040515 A040516 A040513

Adjacent sequences: A317320 A317321 A317322 * A317324 A317325 A317326

Keyword

nonn,easy,mult,changed

Author

Omar E. Pol, Jul 25 2018

Status

approved