A317324 Multiples of 24 and odd numbers interleaved.

0, 1, 24, 3, 48, 5, 72, 7, 96, 9, 120, 11, 144, 13, 168, 15, 192, 17, 216, 19, 240, 21, 264, 23, 288, 25, 312, 27, 336, 29, 360, 31, 384, 33, 408, 35, 432, 37, 456, 39, 480, 41, 504, 43, 528, 45, 552, 47, 576, 49, 600, 51, 624, 53, 648, 55, 672, 57, 696, 59, 720, 61, 744, 63, 768, 65, 792, 67, 816, 69

Offset

0,3

Comments

Partial sums give the generalized 28-gonal numbers (A303812).

a(n) is also the length of the n-th line segment of the rectangular spiral whose vertices are the generalized 28-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) = 24*n, a(2n+1) = 2*n + 1.

G.f.: x*(1 + 24*x + x^2)/((1-x)^2*(1+x)^2). - Vincenzo Librandi, Jul 28 2018

a(n) = 2*a(n-2) - a(n-4) for n>3. - Colin Barker, Jul 29 2018

Multiplicative with a(2^e) = 3*2^(e+2), and a(p^e) = p^e for an odd prime p. - Amiram Eldar, Oct 14 2023

Dirichlet g.f.: zeta(s-1) * (1 + 11*2^(1-s)). - Amiram Eldar, Oct 26 2023

Mathematica

Table[If[EvenQ[n], 24 (n/2), n], {n, 0, 70}] (* Vincenzo Librandi, Jul 28 2018 *)
With[{nn=40}, Riffle[24*Range[0, nn], 2*Range[0, nn]+1]] (* or *) LinearRecurrence[ {0, 2, 0, -1}, {0, 1, 24, 3}, 80] (* Harvey P. Dale, Jul 06 2019 *)

Prog

(Magma) &cat[[24*n, 2*n + 1]: n in [0..30]]; // Vincenzo Librandi, Jul 28 2018
(PARI) concat(0, Vec(x*(1 + 24*x + x^2) / ((1 - x)^2*(1 + x)^2) + O(x^60))) \\ Colin Barker, Jul 29 2018

Crossrefs

Cf. A008606 and A005408 interleaved.

Column 24 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. A303812.

Sequence in context: A070707 A126653 A040567 * A040561 A040562 A267285

Adjacent sequences: A317321 A317322 A317323 * A317325 A317326 A317327

Keyword

nonn,easy,mult

Author

Omar E. Pol, Jul 25 2018

Status

approved