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A317321
Multiples of 21 and odd numbers interleaved.
4
0, 1, 21, 3, 42, 5, 63, 7, 84, 9, 105, 11, 126, 13, 147, 15, 168, 17, 189, 19, 210, 21, 231, 23, 252, 25, 273, 27, 294, 29, 315, 31, 336, 33, 357, 35, 378, 37, 399, 39, 420, 41, 441, 43, 462, 45, 483, 47, 504, 49, 525, 51, 546, 53, 567, 55, 588, 57, 609, 59, 630, 61, 651, 63, 672, 65, 693, 67, 714, 69
OFFSET
0,3
COMMENTS
Partial sums give the generalized 25-gonal numbers (A303304).
a(n) is also the length of the n-th line segment of the rectangular spiral whose vertices are the generalized 25-gonal numbers.
FORMULA
a(2n) = 21*n, a(2n+1) = 2*n + 1.
Multiplicative with a(2^e) = 21*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 + 19/2^s). - Amiram Eldar, Oct 26 2023
MATHEMATICA
a[n_] := If[OddQ[n], n, 21*n/2]; Array[a, 70, 0] (* Amiram Eldar, Oct 14 2023 *)
PROG
(PARI) concat(0, Vec(x*(1 + 21*x + x^2) / ((1 - x)^2*(1 + x)^2) + O(x^60))) \\ Colin Barker, Jul 29 2018
CROSSREFS
Cf. A008603 and A005408 interleaved.
Column 21 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. A303304.
Sequence in context: A035419 A218249 A040433 * A080472 A118389 A077690
KEYWORD
nonn,easy,mult
AUTHOR
Omar E. Pol, Jul 25 2018
STATUS
approved