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 A297675 a(n) = 3*(n^2+n-4)/2. 0
 3, 12, 24, 39, 57, 78, 102, 129, 159, 192, 228, 267, 309, 354, 402, 453, 507, 564, 624, 687, 753, 822, 894, 969, 1047, 1128, 1212, 1299, 1389, 1482, 1578, 1677, 1779, 1884, 1992, 2103, 2217, 2334, 2454, 2577, 2703, 2832, 2964, 3099, 3237, 3378, 3522, 3669, 3819, 3972, 4128 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Also the number of chords in the n-triangular grid graph for n >=2. LINKS Eric Weisstein's World of Mathematics, Graph Chord Eric Weisstein's World of Mathematics, Triangular Grid Graph Index entries for linear recurrences with constant coefficients, signature (3, -3, 1). FORMULA a(n) = 3*a(n-1) - 3*a(n-2) + a(n-1). G.f.: 3*x^2*(-1 - x + x^2)/(-1 + x)^3. MATHEMATICA Table[3 (n^2 + n - 4)/2, {n, 2, 20}] LinearRecurrence[{3, -3, 1}, {3, 12, 24}, 20] CoefficientList[Series[3 (-1 - x + x^2)/(-1 + x)^3, {x, 0, 20}], x] PROG (PARI) a(n) = 3*(n^2+n-4)/2 \\ Felix Fröhlich, Jan 03 2018 (PARI) Vec(3*x^2*(x^2-x-1)/(x-1)^3 + O(x^40)) \\ Felix Fröhlich, Jan 03 2018 CROSSREFS Sequence in context: A012469 A103449 A030571 * A112236 A050180 A319422 Adjacent sequences:  A297672 A297673 A297674 * A297676 A297677 A297678 KEYWORD nonn,easy AUTHOR Eric W. Weisstein, Jan 03 2018 STATUS approved

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Last modified June 18 01:16 EDT 2021. Contains 345098 sequences. (Running on oeis4.)