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A210772 Number of partitions of 2^n into powers of 2 less than or equal to 8. 2
1, 2, 4, 10, 35, 165, 969, 6545, 47905, 366145, 2862209, 22632705, 180007425, 1435853825, 11470030849, 91693092865, 733276217345, 5865135816705, 46916791205889, 375317149057025, 3002468471537665, 24019472891510785, 192154683614691329, 1537233070859485185 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (15,-70,120,-64).

FORMULA

G.f.: -(12*x^5+11*x^4+30*x^3-44*x^2+13*x-1)/Product_{j=0..3} (2^j*x-1).

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

a(n) = 1 + (11*2^(n-3))/3 + 2^(3*n-7)/3 + 4^(n-2) for n>1. - Colin Barker, Jan 26 2018

EXAMPLE

a(3) = 10 because there are 10 partitions of 2^3 = 8 into powers of 2 less than or equal to 8: [1,1,1,1,1,1,1,1], [2,1,1,1,1,1,1], [2,2,1,1,1,1], [2,2,2,1,1], [2,2,2,2], [4,1,1,1,1], [4,2,1,1], [4,2,2], [4,4], [8].

MAPLE

a:= n-> `if`(n<2, 2^n, (Matrix(4, (i, j)-> `if`(i=j-1, 1, `if`(i=4,

     [-64, 120, -70, 15][j], 0)))^(n-2). <<4, 10, 35, 165>>)[1, 1]):

seq(a(n), n=0..30);

PROG

(PARI) Vec((1 - 13*x + 44*x^2 - 30*x^3 - 11*x^4 - 12*x^5) / ((1 - x)*(1 - 2*x)*(1 - 4*x)*(1 - 8*x)) + O(x^40)) \\ Colin Barker, Jan 26 2018

CROSSREFS

Column k=3 of A152977.

Sequence in context: A189591 A189598 A156800 * A125859 A103854 A126941

Adjacent sequences:  A210769 A210770 A210771 * A210773 A210774 A210775

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Mar 26 2012

STATUS

approved

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Last modified July 12 22:46 EDT 2020. Contains 335669 sequences. (Running on oeis4.)