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 A159375 Number of n X n arrays of squares of integers summing to 9. 1
 16, 766, 61184, 3112500, 105851488, 2138413851, 27990555776, 262835331687, 1909384608000, 11319915386120, 56916060868096, 249702337698346, 976762617522160, 3464394870851125, 11290721919375872, 34177386571594701 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS All such sequences have holonomic recurrences (cf. comment in A159359). - Georg Fischer, Feb 17 2022 LINKS R. H. Hardin, Table of n, a(n) for n = 2..100 Index entries for linear recurrences with constant coefficients, signature (19, -171, 969, -3876, 11628, -27132, 50388, -75582, 92378, -92378, 75582, -50388, 27132, -11628, 3876, -969, 171, -19, 1). FORMULA Empirical g.f.: -x-(1+x)*x*(1 - 4*x + 637*x^2 + 47760*x^3 + 2021602*x^4 + 54462984*x^5 + 548532899*x^6 + 2125377516*x^7 + 3360726010*x^8 + 2125377516*x^9 + 548532899*x^10 + 54462984*x^11 + 2021602*x^12 + 47760*x^13 + 637*x^14 - 4*x^15 + x^16)/(-1+x)^19. - Vaclav Kotesovec, Nov 30 2012 a(n) = binomial(n^2,1) + multinomial(n^2,1,2,(n^2-3)) + multinomial(n^2,1,5,n^2-6) + binomial(n^2,9) = (1/362880)*n^18 - (1/10080)*n^16 + (13/8640)*n^14 - (1/240)*n^12 - (1091/17280)*n^10 + (251/480)*n^8 - (95209/90720)*n^6 + (1213/2520)*n^4 + (10/9)*n^2 corresponding to the ways of obtaining 9 as a sum of n^2 squares: 9 + (n^2-1)*0, 2*4 + 1 + (n^2-3)*0, 4 + 5*1 + (n^2 - 6)*0, and 9*1 + (n^2 - 9)*0. - Robert Israel, Dec 18 2023 CROSSREFS Sequence in context: A218297 A339202 A307923 * A221527 A129008 A134183 Adjacent sequences: A159372 A159373 A159374 * A159376 A159377 A159378 KEYWORD nonn AUTHOR R. H. Hardin, Apr 11 2009 STATUS approved

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Last modified September 8 12:42 EDT 2024. Contains 375753 sequences. (Running on oeis4.)