The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A342643 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A342643

a(n) = [x^n] x * Product_{j>=0} (1 + x^(2^j) + n*x^(2^(j+1))).
(history; published version)

#12 by Alois P. Heinz at Wed Mar 17 19:59:44 EDT 2021

STATUS

editing

approved

#11 by Alois P. Heinz at Wed Mar 17 19:59:41 EDT 2021

KEYWORD

nonn,look,new

STATUS

approved

editing

#10 by Alois P. Heinz at Wed Mar 17 19:59:07 EDT 2021

STATUS

editing

approved

#9 by Alois P. Heinz at Wed Mar 17 16:16:51 EDT 2021

NAME

aa

a(n) = [x^n] x * Product_{j>=0} (1 + x^(2^j) + n*x^(2^(j+1))).

#8 by Alois P. Heinz at Wed Mar 17 16:01:02 EDT 2021

LINKS

Alois P. Heinz, <a href="/A342643/b342643.txt">Table of n, a(n) for n = 0..16384</a>

#7 by Alois P. Heinz at Wed Mar 17 15:57:06 EDT 2021

MAPLE

`if`(p=1, i*0, b(h, i)+, i*b(h+1, , i), +b(h, +1, i)))(iquo(n, 2, 'p')))

#6 by Alois P. Heinz at Wed Mar 17 15:54:26 EDT 2021

CROSSREFS

Cf. A002487.

#5 by Alois P. Heinz at Wed Mar 17 15:51:25 EDT 2021

FORMULA

a(2^n) = 1 for n >= 0.

#4 by Alois P. Heinz at Wed Mar 17 15:50:12 EDT 2021

MAPLE

b:= proc(n, ki) option remember; `if`(n<2, n, (qh->

`if`(dp=1, ki*b(q, kh, i)+b(qh+1, ki), b(q, kh, i)))(iquo(n, 2, 'dp')))

seq(a(n), n=0..5055);

#3 by Alois P. Heinz at Wed Mar 17 15:45:52 EDT 2021

DATA

0, 1, 1, 4, 1, 11, 7, 57, 1, 28, 21, 265, 13, 365, 211, 3616, 1, 69, 55, 1141, 41, 1828, 1013, 25439, 25, 1951, 1405, 41608, 813, 50519, 27931, 954305, 1, 166, 137, 5041, 109, 8363, 4447, 182638, 81, 10251, 7183, 327403, 3961, 372736, 198997, 9971521, 49, 9801

OFFSET

0,14

MAPLE

b:= proc(n, k) option remember; `if`(n<2, n, (q->

`if`(d=1, k*b(q, k)+b(q+1, k), b(q, k)))(iquo(n, 2, 'd')))

end:

a:= n-> b(n$2):

seq(a(n), n=0..50);