A068789 S(n; 2,0) where S(n; t,s) is the number of length n 4-ary strings whose digits sum to t mod 4 and whose sum of products of all pairs of digits sum to s mod 4.

1, 2, 4, 16, 56, 272, 1184, 4608, 17536, 65792, 254464, 1017856, 4130816, 16781312, 67641344, 270532608, 1077968896, 4295032832, 17146445824, 68585783296, 274609995776, 1099512676352, 4400196091904, 17600775979008, 70385932435456, 281474993487872

Offset

1,2

Links

Table of n, a(n) for n=1..26.

Max Alekseyev, PARI/GP scripts for miscellaneous math problems

F. Ruskey, 4-ary strings with given trace and subtrace

Formula

S(n; t, s) = S(n-1; t, s) + S(n-1; t+3, s+3t+1) + S(n-1; t+2, s+2t) + S(n-1; t+1, s+t+1).

Empirical g.f.: x*(1-8*x+24*x^2-24*x^3-24*x^4+32*x^5+64*x^6-192*x^7) / ((1-2*x)*(1-4*x)*(1-4*x+8*x^2)*(1+16*x^4)). - Colin Barker, Feb 21 2016

Crossrefs

Cf. A068620, A068711, A068774, A068777, A068786, A068778, A068787, A068788, A068790.

Sequence in context: A053503 A308381 A153957 * A009624 A009161 A009290

Adjacent sequences: A068786 A068787 A068788 * A068790 A068791 A068792

Keyword

nonn,base

Author

Frank Ruskey, Mar 29 2002

Extensions

Terms a(11) onward from Max Alekseyev, Apr 09 2013

Status

approved