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A071646
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Number of base 4 n-digit numbers with digit sum n.
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0
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1, 2, 6, 19, 61, 201, 672, 2269, 7723, 26452, 91058, 314766, 1091884, 3798900, 13251136, 46325285, 162268775, 569385098, 2001012474, 7042014879, 24813529581, 87533417037, 309107111536, 1092585807044, 3865270781236
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| a(n)=[x^n] (1+x+x^2+x^3)^n-(1+x+x^2+x^3)^(n-1). - Michael Somos, Jul 19 2002
a(n)*790*(2*n^2-n) = a(n-1)*(-16328*n^4+137200*n^3-400977*n^2+489925*n-207450)+a(n-2)*(44902*n^4-399751*n^3+1267117*n^2-1672482*n+769980)+a(n-3)*4*(n-3)*(8164*n^3-52272*n^2+115397*n-81223)+a(n-4)*16*(n-4)*(n-3)*(4082*n^2-11849*n+8529), n>2. - Michael Somos, Jul 19 2002
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PROG
| (PARI) a(n)=local(y=(x^4-1)/(x-1)); if(n<0, 0, polcoeff(y^n-y^(n-1), n))
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CROSSREFS
| Cf. A071976, A005773.
Sequence in context: A138747 A052975 A035929 * A114627 A148464 A148465
Adjacent sequences: A071643 A071644 A071645 * A071647 A071648 A071649
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KEYWORD
| nonn
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AUTHOR
| John W. Layman (layman(AT)math.vt.edu), Jun 22 2002
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