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A317315
Multiples of 15 and odd numbers interleaved.
4
0, 1, 15, 3, 30, 5, 45, 7, 60, 9, 75, 11, 90, 13, 105, 15, 120, 17, 135, 19, 150, 21, 165, 23, 180, 25, 195, 27, 210, 29, 225, 31, 240, 33, 255, 35, 270, 37, 285, 39, 300, 41, 315, 43, 330, 45, 345, 47, 360, 49, 375, 51, 390, 53, 405, 55, 420, 57, 435, 59, 450, 61, 465, 63, 480, 65, 495, 67, 510, 69
OFFSET
0,3
COMMENTS
Partial sums give the generalized 19-gonal numbers (A303813).
a(n) is also the length of the n-th line segment of the rectangular spiral whose vertices are the generalized 19-gonal numbers.
FORMULA
a(2n) = 15*n, a(2n+1) = 2*n + 1.
From Colin Barker, Jul 29 2018: (Start)
G.f.: x*(1 + 15*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) = 15*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 + 13/2^s). - Amiram Eldar, Oct 25 2023
MATHEMATICA
a[n_] := If[OddQ[n], n, 15*n/2]; Array[a, 70, 0] (* Amiram Eldar, Oct 14 2023 *)
PROG
(PARI) concat(0, Vec(x*(1 + 15*x + x^2) / ((1 - x)^2*(1 + x)^2) + O(x^60))) \\ Colin Barker, Jul 29 2018
CROSSREFS
Cf. A008597 and A005408 interleaved.
Column 15 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. A303813.
Sequence in context: A248129 A256527 A040219 * A330361 A291157 A040216
KEYWORD
nonn,easy,mult
AUTHOR
Omar E. Pol, Jul 25 2018
STATUS
approved