A317317 Multiples of 17 and odd numbers interleaved.

0, 1, 17, 3, 34, 5, 51, 7, 68, 9, 85, 11, 102, 13, 119, 15, 136, 17, 153, 19, 170, 21, 187, 23, 204, 25, 221, 27, 238, 29, 255, 31, 272, 33, 289, 35, 306, 37, 323, 39, 340, 41, 357, 43, 374, 45, 391, 47, 408, 49, 425, 51, 442, 53, 459, 55, 476, 57, 493, 59, 510, 61, 527, 63, 544, 65, 561, 67, 578, 69

Offset

0,3

Comments

Partial sums give the generalized 21-gonal numbers (A303298).

a(n) is also the length of the n-th line segment of the rectangular spiral whose vertices are the generalized 21-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) = 17*n, a(2n+1) = 2*n + 1.

From Colin Barker, Jul 29 2018: (Start)

G.f.: x*(1 + 17*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) = 17*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 + 15/2^s). - Amiram Eldar, Oct 25 2023

Mathematica

With[{nn=40}, Riffle[17*Range[0, nn], 2*Range[0, nn]+1]] (* or *) LinearRecurrence[ {0, 2, 0, -1}, {0, 1, 17, 3}, 80] (* Harvey P. Dale, Jun 06 2020 *)

Prog

(PARI) concat(0, Vec(x*(1 + 17*x + x^2) / ((1 - x)^2*(1 + x)^2) + O(x^60))) \\ Colin Barker, Jul 29 2018

Crossrefs

Cf. A008599 and A005408 interleaved.

Column 17 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. A303298.

Sequence in context: A040282 A139728 A336485 * A212602 A174380 A040278

Adjacent sequences: A317314 A317315 A317316 * A317318 A317319 A317320

Keyword

nonn,easy,mult

Author

Omar E. Pol, Jul 25 2018

Status

approved