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 A210376 Number of 2 X 2 matrices with all terms in {0,1,...,n} and (sum of terms) = n + 4. 3
 0, 0, 10, 40, 85, 140, 206, 284, 375, 480, 600, 736, 889, 1060, 1250, 1460, 1691, 1944, 2220, 2520, 2845, 3196, 3574, 3980, 4415, 4880, 5376, 5904, 6465, 7060, 7690, 8356, 9059, 9800, 10580, 11400, 12261, 13164, 14110, 15100, 16135, 17216 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A210376 is also the number of 2 X 2 matrices with all terms in {0,1,...,n} and (sum of terms) = 3n - 4. See A210000 for a guide to related sequences. LINKS FORMULA Conjectures from Colin Barker, Dec 07 2017: (Start) G.f.: x^2*(10 - 15*x^2 + 6*x^4) / (1 - x)^4. a(n) = (-270 + 107*n + 18*n^2 + n^3) / 6 for n>2. a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4. (End) MATHEMATICA a = 0; b = n; z1 = 45; t[n_] := t[n] = Flatten[Table[w + x + y + z, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]] c[n_, k_] := c[n, k] = Count[t[n], k] Table[c[n, n + 4], {n, 0, z1}]    (* A210376 *) Table[c[n, 3 n - 4], {n, 0, z1}]  (* A210376 *) CROSSREFS Cf. A210000. Sequence in context: A306830 A305131 A217073 * A060317 A033583 A131037 Adjacent sequences:  A210373 A210374 A210375 * A210377 A210378 A210379 KEYWORD nonn AUTHOR Clark Kimberling, Mar 20 2012 STATUS approved

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Last modified April 22 07:26 EDT 2021. Contains 343163 sequences. (Running on oeis4.)