|
Search: id:A071646
|
|
|
| A071646 |
|
Number of base 4 n-digit numbers with digit sum n. |
|
+0
1
|
|
| 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; listen)
|
|
|
OFFSET
|
1,2
|
|
|
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
|
|
PROGRAM
|
(PARI) a(n)=local(y=(x^4-1)/(x-1)); if(n<0, 0, polcoeff(y^n-y^(n-1), n))
|
|
CROSSREFS
|
Cf. A071976, A005773.
Sequence in context: A138747 A052975 A035929 this_sequence A114627 A094817 A033565
Adjacent sequences: A071643 A071644 A071645 this_sequence A071647 A071648 A071649
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
John W. Layman (layman(AT)math.vt.edu), Jun 22 2002
|
|
|
Search completed in 0.002 seconds
|
