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 A180670 a(n) = a(n-1)+a(n-2)+a(n-3)+(8*n^3-48*n^2+112*n-96)/3 with a(0)=0, a(1)=0 and a(2)=1. 5
 0, 0, 1, 9, 42, 140, 383, 925, 2056, 4316, 8705, 17069, 32810, 62192, 116743, 217673, 404000, 747496, 1380177, 2544865, 4688186, 8631620, 15886111, 29230725, 53776968, 98926372, 181971057, 334716197, 615660634, 1132400520 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The a(n+2) represent the Kn15 and Kn25 sums of the square array of Delannoy numbers A008288. See A180662 for the definition of these knight and other chess sums. LINKS Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-3,3,-3,1). FORMULA a(n) = a(n-1)+a(n-2)+a(n-3)+(8*n^3-48*n^2+112*n-96)/3 with a(0)=0, a(1)=0 and a(2)=1. a(n) = a(n-1)+A001590(n+7)-(12+4*n+4*n^2) with a(0)=0. a(n) = sum(A008412(m)*A000073(n-m),m=0..n). a(n+2) = add(A008288(n-k+4,k+4),k=0..floor(n/2)). GF(x) = (x^2*(1+x)^4)/((1-x)^4*(1-x-x^2-x^3)). MAPLE nmax:=29: 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)+(8*n^3-48*n^2+112*n-96)/3 od: seq(a(n), n=0..nmax); MATHEMATICA RecurrenceTable[{a[0]==a[1]==0, a[2]==1, a[n]==a[n-1]+a[n-2]+a[n-3]+(8n^3-48n^2+112n-96)/3}, a, {n, 30}] (* or *) LinearRecurrence[{5, -9, 7, -3, 3, -3, 1}, {0, 0, 1, 9, 42, 140, 383}, 30] (* Harvey P. Dale, Dec 04 2019 *) CROSSREFS Cf. A000073 (Kn11 & Kn21), A089068 (Kn12 & Kn22), A180668 (Kn13 & Kn23), A180669 (Kn14 & Kn24), A180670 (Kn15 & Kn25). Sequence in context: A061927 A292481 A051923 * A268262 A293101 A084899 Adjacent sequences:  A180667 A180668 A180669 * A180671 A180672 A180673 KEYWORD easy,nonn AUTHOR Johannes W. Meijer, Sep 21 2010 STATUS approved

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Last modified July 6 15:30 EDT 2022. Contains 355110 sequences. (Running on oeis4.)