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A317324
Multiples of 24 and odd numbers interleaved.
4
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.
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
KEYWORD
nonn,easy,mult
AUTHOR
Omar E. Pol, Jul 25 2018
STATUS
approved