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 A213585 Principal diagonal of the convolution array A213584. 3
 1, 7, 22, 54, 116, 232, 443, 821, 1490, 2664, 4710, 8256, 14373, 24883, 42878, 73594, 125880, 214664, 365087, 619425, 1048666, 1771852, 2988362, 5031744, 8459401, 14201887, 23811238, 39873726, 66695420, 111440104, 186016835 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Clark Kimberling, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (4,-4,-2,4,0,-1). FORMULA a(n) = 4*a(n-1) - 4*a(n-2) - 2*a(n-3) + 4*a(n-4) + a(n-5). G.f.: x*(1 + 3*x - 2*x^2 - 4*x^3 - 2*x^4)/(1 - 2*x + x^3)^2. a(n) = Fibonacci(n+4) + n*Fibonacci(n+3) - (4*n + 3). - G. C. Greubel, Jul 08 2019 MATHEMATICA (* First program *) b[n_]:= Fibonacci[n+1]; c[n_]:= n; T[n_, k_]:= Sum[b[k-i] c[n+i], {i, 0, k-1}] TableForm[Table[T[n, k], {n, 1, 10}, {k, 1, 10}]] Flatten[Table[T[n-k+1, k], {n, 12}, {k, n, 1, -1}]] (* A213584 *) r[n_]:= Table[T[n, k], {k, 40}] (* columns of antidiagonal triangle *) d = Table[T[n, n], {n, 1, 40}] (* A213585 *) s[n_]:= Sum[T[i, n+1-i], {i, 1, n}] s1 = Table[s[n], {n, 1, 50}] (* A213586 *) (* Second program *) Table[Fibonacci[n+4] + n*Fibonacci[n+3] -4*n-3, {n, 40}] (* G. C. Greubel, Jul 08 2019 *) PROG (PARI) vector(40, n, f=fibonacci; f(n+4) +n*f(n+3) -(4*n+3)) \\ G. C. Greubel, Jul 08 2019 (Magma) F:=Fibonacci; [F(n+4) +n*F(n+3) -(4*n+3): n in [1..40]]; // G. C. Greubel, Jul 08 2019 (Sage) f=fibonacci; [f(n+4) +n*f(n+3) -(4*n+3) for n in (1..40)] # G. C. Greubel, Jul 08 2019 (GAP) F:=Fibonacci;; List([1..40], n-> F(n+4) +n*F(n+3) -(4*n+3)) # G. C. Greubel, Jul 08 2019 CROSSREFS Cf. A000045, A213500, A213584. Sequence in context: A101120 A151717 A188377 * A308579 A246831 A354430 Adjacent sequences: A213582 A213583 A213584 * A213586 A213587 A213588 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jun 18 2012 STATUS approved

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Last modified June 6 03:09 EDT 2023. Contains 363138 sequences. (Running on oeis4.)