A317320 Multiples of 20 and odd numbers interleaved.

0, 1, 20, 3, 40, 5, 60, 7, 80, 9, 100, 11, 120, 13, 140, 15, 160, 17, 180, 19, 200, 21, 220, 23, 240, 25, 260, 27, 280, 29, 300, 31, 320, 33, 340, 35, 360, 37, 380, 39, 400, 41, 420, 43, 440, 45, 460, 47, 480, 49, 500, 51, 520, 53, 540, 55, 560, 57, 580, 59, 600, 61, 620, 63, 640, 65, 660, 67, 680, 69

Offset

0,3

Comments

Partial sums give the generalized 24-gonal numbers (A303814).

a(n) is also the length of the n-th line segment of the rectangular spiral whose vertices are the generalized 24-gonal numbers.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Formula

a(n) = n, if n is odd.

a(n) = 10*n, if n is even.

a(2n) = 20*n, a(2n+1) = 2*n + 1.

From Colin Barker, Jul 29 2018: (Start)

G.f.: x*(1 + 20*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) = 5*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 + 9*2^(1-s)). - Amiram Eldar, Oct 26 2023

Mathematica

With[{nn=40}, Riffle[20*Range[0, nn], Range[1, 2*nn+1, 2]]] (* Harvey P. Dale, Feb 16 2020 *)

Prog

(PARI) concat(0, Vec(x*(1 + 20*x + x^2) / ((1 - x)^2*(1 + x)^2) + O(x^60))) \\ Colin Barker, Jul 29 2018

Crossrefs

Cf. A008602 and A005408 interleaved.

Column 20 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. A303814.

Sequence in context: A070645 A248136 A040392 * A327701 A337157 A040388

Adjacent sequences: A317317 A317318 A317319 * A317321 A317322 A317323

Keyword

nonn,easy,mult

Author

Omar E. Pol, Jul 25 2018

Status

approved