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A029120 Expansion of 1/((1-x)(1-x^7)(1-x^8)(1-x^12)). 1
1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 4, 4, 5, 6, 7, 7, 7, 8, 9, 10, 11, 12, 14, 14, 15, 16, 18, 19, 20, 22, 24, 25, 26, 28, 31, 32, 34, 36, 39, 40, 42, 45, 48, 50, 52, 55, 59, 61, 64, 67, 71, 73, 76, 80, 85, 88, 91, 95, 100 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Number of partitions of n into parts 1, 7, 8, and 12. [Joerg Arndt, Aug 14 2013]

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

FORMULA

a(0)=1, a(1)=1, a(2)=1, a(3)=1, a(4)=1, a(5)=1, a(6)=1, a(7)=2, a(8)=3, a(9)=3, a(10)=3, a(11)=3, a(12)=4, a(13)=4, a(14)=5, a(15)=6, a(16)=7, a(17)=7, a(18)=7, a(19)=8, a(20)=9, a(21)=10, a(22)=11, a(23)=12, a(24)=14, a(25)=14, a(26)=15, a(27)=16; for n>27, a(n) = a(n-1) +a(n-7) -a(n-9) +a(n-12) -a(n-13) -a(n-15) +a(n-16) -a(n-19) +a(n-21) +a(n-27) -a(n-28). - Harvey P. Dale, Aug 13 2013

MATHEMATICA

CoefficientList[Series[1/((1 - x) (1 - x^7) (1 - x^8) (1 - x^12)), {x, 0, 60}], x] (* or *) LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 1, -1, 0, -1, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 1, -1}, {1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 4, 4, 5, 6, 7, 7, 7, 8, 9, 10, 11, 12, 14, 14, 15, 16}, 70] (* Harvey P. Dale, Aug 13 2013 *)

CROSSREFS

Sequence in context: A194227 A194819 A194235 * A078428 A337634 A316355

Adjacent sequences:  A029117 A029118 A029119 * A029121 A029122 A029123

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified September 28 06:22 EDT 2022. Contains 357063 sequences. (Running on oeis4.)