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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. 9
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 18 03:03 EDT 2021. Contains 343994 sequences. (Running on oeis4.)