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A068745 Number of potential flows in 4 X 4 array with integer velocities in -n..n, i.e., number of 4 X 4 arrays with adjacent elements differing by no more than n, counting arrays differing by a constant only once. 21
1, 690437, 1133641543, 164185416899, 6913624013061, 138190481342321, 1678843050246451, 14285299502131463, 93044501704039945, 492225938556374973, 2204710243834695807, 8617480381892283531 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..11.

FORMULA

Let y = 2*n - 1; it appears that a(n) = y*(2623243666*y^14 + 9598591135*y^12 + 17180805187*y^10 + 20342655905*y^8 + 17636121503*y^6 + 10907793260*y^4 + 3135618144*y^2 + 304819200)/81729648000. - R. H. Hardin, Jan 01 2007

CROSSREFS

2 X 2 A063496, 3 X 3 A068744, 5 X 5 A068746, 6 X 6 A068747, by velocity limit 1..14 A068748-A068761, solenoidal flows A068722-A068738.

Cf. 4 X 4 this sequence (degree 4*4-1) with factor 2n-1 ; 3 X 3 A068744 (degree 3*3-1) with factor (2n-1)^2 ; 2 X 2 A063496 (degree 2*2-1) with factor 2n-1.

Sequence in context: A254773 A254780 A254726 * A010084 A209735 A273970

Adjacent sequences:  A068742 A068743 A068744 * A068746 A068747 A068748

KEYWORD

nonn

AUTHOR

R. H. Hardin, Feb 27 2002

STATUS

approved

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Last modified December 5 04:53 EST 2021. Contains 349530 sequences. (Running on oeis4.)