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A317322
Multiples of 22 and odd numbers interleaved.
4
0, 1, 22, 3, 44, 5, 66, 7, 88, 9, 110, 11, 132, 13, 154, 15, 176, 17, 198, 19, 220, 21, 242, 23, 264, 25, 286, 27, 308, 29, 330, 31, 352, 33, 374, 35, 396, 37, 418, 39, 440, 41, 462, 43, 484, 45, 506, 47, 528, 49, 550, 51, 572, 53, 594, 55, 616, 57, 638, 59, 660, 61, 682, 63, 704, 65, 726, 67, 748, 69
OFFSET
0,3
COMMENTS
Partial sums give the generalized 26-gonal numbers (A316724).
a(n) is also the length of the n-th line segment of the rectangular spiral whose vertices are the generalized 26-gonal numbers.
FORMULA
a(2n) = 22*n, a(2n+1) = 2*n + 1.
From Colin Barker, Jul 29 2018: (Start)
G.f.: x*(1 + 22*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) = 11*2^e, and a(p^e) = p^e for an odd prime p. - Amiram Eldar, Oct 14 2023
Dirichlet g.f.: zeta(s-1) * (1 + 5*2^(2-s)). - Amiram Eldar, Oct 26 2023
MATHEMATICA
Module[{nn=40}, Riffle[22Range[0, nn], Range[1, 2nn, 2]]] (* or *) LinearRecurrence[ {0, 2, 0, -1}, {0, 1, 22, 3}, 80] (* Harvey P. Dale, Dec 12 2021 *)
PROG
(PARI) concat(0, Vec(x*(1 + 22*x + x^2) / ((1 - x)^2*(1 + x)^2) + O(x^60))) \\ Colin Barker, Jul 29 2018
CROSSREFS
Cf. A008604 and A005408 interleaved.
Column 22 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. A316724.
Sequence in context: A040475 A065662 A174735 * A040470 A040471 A018817
KEYWORD
nonn,easy,mult
AUTHOR
Omar E. Pol, Jul 25 2018
STATUS
approved