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A317319
Multiples of 19 and odd numbers interleaved.
4
0, 1, 19, 3, 38, 5, 57, 7, 76, 9, 95, 11, 114, 13, 133, 15, 152, 17, 171, 19, 190, 21, 209, 23, 228, 25, 247, 27, 266, 29, 285, 31, 304, 33, 323, 35, 342, 37, 361, 39, 380, 41, 399, 43, 418, 45, 437, 47, 456, 49, 475, 51, 494, 53, 513, 55, 532, 57, 551, 59, 570, 61, 589, 63, 608, 65, 627, 67, 646, 69
OFFSET
0,3
COMMENTS
Partial sums give the generalized 23-gonal numbers (A303303).
a(n) is also the length of the n-th line segment of the rectangular spiral whose vertices are the generalized 23-gonal numbers.
FORMULA
a(2n) = 19*n, a(2n+1) = 2*n + 1.
From Colin Barker, Jul 29 2018: (Start)
G.f.: x*(1 + 19*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) = 19*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 + 17/2^s). - Amiram Eldar, Oct 26 2023
MATHEMATICA
a[n_] := If[OddQ[n], n, 19*n/2]; Array[a, 70, 0] (* Amiram Eldar, Oct 14 2023 *)
PROG
(PARI) concat(0, Vec(x*(1 + 19*x + x^2) / ((1 - x)^2*(1 + x)^2) + O(x^60))) \\ Colin Barker, Jul 29 2018
CROSSREFS
Cf. A008601 and A005408 interleaved.
Column 19 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. A303303.
Sequence in context: A349406 A040353 A128160 * A002206 A040349 A274249
KEYWORD
nonn,easy,mult
AUTHOR
Omar E. Pol, Jul 25 2018
STATUS
approved