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 A276914 Subsequence of triangular numbers obtained by adding a square and two smaller triangles, a(n) = n^2 + 2*A000217(A052928(n)). 3
 0, 1, 10, 15, 36, 45, 78, 91, 136, 153, 210, 231, 300, 325, 406, 435, 528, 561, 666, 703, 820, 861, 990, 1035, 1176, 1225, 1378, 1431, 1596, 1653, 1830, 1891, 2080, 2145, 2346, 2415, 2628, 2701, 2926, 3003, 3240, 3321, 3570, 3655, 3916, 4005, 4278, 4371, 4656 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS All terms of this sequence are triangular numbers. Graphically, for each term of the sequence, one corner of the square will be part of the corresponding triangle's hypotenuse if the term is an odd number. Otherwise, it will not be part of it. a(A276915(n)) is a triangular pentagonal number. a(A079291(n)) is a triangular square number, as A275496 is a subsequence of this. LINKS Daniel Poveda Parrilla, Table of n, a(n) for n = 0..10000 Daniel Poveda Parrilla, Illustration of initial terms Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1). FORMULA a(n) = n^2 + 2*A000217(A052928(n)). a(n) = A000217(A042948(n)). a(n) = n*(2*n + (-1)^n). a(n) = n*A168277(n + 1). a(n) = n*A016813(A004526(n)). From Colin Barker, Sep 23 2016: (Start) G.f.: x*(1 + 9*x + 3*x^2 + 3*x^3) / ((1 - x)^3*(1 + x)^2). a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>4. a(n) = n*(2*n+1) for n even. a(n) = n*(2*n-1) for n odd. (End) MATHEMATICA Table[n (2 n + (-1)^n), {n, 0, 48}] (* Michael De Vlieger, Sep 23 2016 *) PROG (PARI) concat(0, Vec(x*(1+9*x+3*x^2+3*x^3)/((1-x)^3*(1+x)^2) + O(x^50))) \\ Colin Barker, Sep 23 2016 CROSSREFS Cf. A000217, A004526, A016813, A042948, A052928, A079291, A168277, A275496, A276915. Sequence in context: A037379 A055049 A128703 * A078818 A194267 A261853 Adjacent sequences:  A276911 A276912 A276913 * A276915 A276916 A276917 KEYWORD nonn,easy AUTHOR Daniel Poveda Parrilla, Sep 22 2016 STATUS approved

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Last modified July 14 00:22 EDT 2020. Contains 335716 sequences. (Running on oeis4.)