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 A180669 a(n) = a(n-1)+a(n-2)+a(n-3)+4*n^2-16*n+18 with a(0)=0, a(1)=0 and a(2)=1. 5
 0, 0, 1, 7, 26, 72, 171, 371, 760, 1500, 2889, 5475, 10266, 19116, 35435, 65495, 120832, 222664, 410017, 754671, 1388650, 2554784, 4699707, 8644907, 15901336, 29248068, 53796617, 98948523, 181995914, 334743972, 615691547 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The a(n+2) represent the Kn14 and Kn24 sums of the square array of Delannoy numbers A008288. See A180662 for the definition of these knight and other chess sums. LINKS Table of n, a(n) for n=0..30. Index entries for linear recurrences with constant coefficients, signature (4,-5,2,-1,2,-1). FORMULA a(n) = a(n-1)+a(n-2)+a(n-3)+4*(n-2)^2+2 with a(0)=0, a(1)=0 and a(2)=1. a(n) = a(n-1)+A001590(n+5)-2-4*n with a(0)=0. a(n) = Sum_{m=0..n} A005899(m)*A000073(n-m). a(n+2) = Sum_{k=0..floor(n/2)} A008288(n-k+3,k+3). GF(x) = (x^2*(1+x)^3)/((1-x)^3*(1-x-x^2-x^3)). From Bruno Berselli, Sep 23 2010: (Start) a(n) = 3*a(n-1)-2a(n-2)-a(n-4)+a(n-5)+8 for n>4. a(n)-4*a(n-1)+5a(n-2)-2*a(n-3)+a(n-4)-2*a(n-5)+a(n-6) = 0 for n>5. (End) MAPLE nmax:=30: a(0):=0: a(1):=0: a(2):=1: for n from 3 to nmax do a(n):= a(n-1)+a(n-2)+a(n-3)+4*(n-2)^2+2 od: seq(a(n), n=0..nmax); CROSSREFS Cf. A000073 (Kn11 & Kn21), A089068 (Kn12 & Kn22), A180668 (Kn13 & Kn23), A180669 (Kn14 & Kn24), A180670 (Kn15 & Kn25). Cf. A000073, A005899, A008288. Sequence in context: A006325 A053346 A227021 * A027964 A183957 A078501 Adjacent sequences: A180666 A180667 A180668 * A180670 A180671 A180672 KEYWORD easy,nonn AUTHOR Johannes W. Meijer, Sep 21 2010 STATUS approved

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Last modified February 29 19:20 EST 2024. Contains 370428 sequences. (Running on oeis4.)