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A317323 Multiples of 23 and odd numbers interleaved. 4
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,easy,mult
AUTHOR
Omar E. Pol, Jul 25 2018
STATUS
approved

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Last modified July 22 06:07 EDT 2024. Contains 374481 sequences. (Running on oeis4.)