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Search: id:A025795
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| A025795 |
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Expansion of 1/((1-x^2)(1-x^3)(1-x^5)). |
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+0
3
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| 1, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9, 9, 11, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 21, 23, 24, 25, 27, 28, 29, 31, 32, 34, 35, 37, 38, 40, 42, 43, 45, 47, 48, 51, 52, 54, 56, 58, 60, 62, 64, 66, 68, 71, 72, 75, 77, 79, 82, 84, 86, 89, 91, 94, 96, 99, 101, 104
(list; graph; listen)
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OFFSET
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0,6
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COMMENT
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a(n) = number of ways to pay n dollars with coins of two, three and five dollars. E.g. a(0)=1 because there is one way to pay : with no coin ; a(1)=0 no possibility ; a(2)=1 (2=1*2) ; a(3)=1 (3=1*3) ; a(4)=1 (4=2*2) a(5)=2 (5=3+2=1*5) ... - Richard Choulet (richardchoulet(AT)yahoo.fr), Jan 20 2008
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FORMULA
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G.f.: 1/((1-x^2)(1-x^3)(1-x^5)).
Let [b(1); b(2); ...; b(p)] denote a periodic sequemce: e.g. [0; 1] definies the sequence c such that c(0)=c(2)=..c(2*k)=0 and c(1)=c(3)=...c(2*k+1)=1. Then a(n)=0.25*[0; 1]-(1/3)*[1; 0; 0]+(1/5)*[0; 1; 1; 0; 3]+((n+1)*(n+2)/60)+(7*(n+1)/60). - Richard Choulet (richardchoulet(AT)yahoo.fr), Jan 20 2008
If ||A|| is the nearest number to A (A not a half integer) we have also : a(n)=||((n+1)*(n+9)/60)+(1/5)[0; 1; 1; 0; 3]. - Richard Choulet (richardchoulet(AT)yahoo.fr), Jan 20 2008
a(n)=(77/360)+(7*(n+1)/60)+((n+2)*(n+1)/60)+((-1)^n/8)-(2/9)*cos((2*(n+2)*Pi)/3)+(4/(5*5^0.5+25))*cos((2*n*Pi)/5)-(4/(5*5^0.5-25))*cos((4*n*Pi)/5) - Richard Choulet (richardchoulet(AT)yahoo.fr), Jan 20 2008
Euler transform of length 5 sequence [ 0, 1, 1, 0, 1]. - Michael Somos Feb 05 2008
a(-10-n) = a(n). - Michael Somos Feb 25 2008
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EXAMPLE
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1 + q^2 + q^3 + q^4 + 2*q^5 + 2*q^6 + 2*q^7 + 3*q^8 + 3*q^9 + 4*q^10 + ...
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PROGRAM
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(PARI) {a(n) = (n^2 + 10*n + 1 - n%2 * 13) \60 + 1} /* Michael Somos Feb 05 2008 */
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CROSSREFS
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Adjacent sequences: A025792 A025793 A025794 this_sequence A025796 A025797 A025798
Sequence in context: A112995 A078452 A135636 this_sequence A051066 A029159 A029099
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KEYWORD
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nonn
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AUTHOR
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njas
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