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A337286 a(n) = Sum_{i=0..n} i^2*T(i)^2, where T(i) = A000073(i) is the i-th tribonacci number. 2
0, 0, 4, 13, 77, 477, 2241, 10522, 47386, 204202, 860302, 3546623, 14357567, 57286271, 225714755, 879795380, 3397426356, 13012405492, 49478890936, 186932228945, 702169068945, 2623863676449, 9758799153349, 36140284390030, 133317609306766, 490032600916766, 1795262239190210, 6557012850772931 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

R. Schumacher, Explicit formulas for sums involving the squares of the first n Tribonacci numbers, Fib. Q., 58:3 (2020), 194-202. (Note that this paper uses an offset for the tribonacci numbers that is different from that used in A000073.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (7,-9,-7,-56,96,108,252,-162,-114,-318,126,-16,136,-36,12,-21,3,-1,1).

FORMULA

G.f.: x^2*(4 - 15*x + 22*x^2 + 83*x^3 - 90*x^4 + 11*x^5 - 128*x^6 - 207*x^7 - 224*x^8 - 233*x^9 - 162*x^10 - 147*x^11 - 58*x^12 - 3*x^13 - 4*x^14 - x^15)/((1-x)*(1 + x + x^2 - x^3)^3*(1 - 3*x - x^2 - x^3)^3). - G. C. Greubel, Nov 22 2021

MATHEMATICA

T[n_]:= T[n]= If[n<2, 0, If[n==2, 1, T[n-1] +T[n-2] +T[n-3]]]; (* A000073 *)

A337286[n_]:= Sum[j^2*T[j]^2, {j, 0, n}];

Table[A337286[n], {n, 0, 50}] (* G. C. Greubel, Nov 22 2021 *)

PROG

(Magma) R<x>:=PowerSeriesRing(Integers(), 40); [0, 0] cat Coefficients(R!( x^2*(4-15*x+22*x^2+83*x^3-90*x^4+11*x^5-128*x^6-207*x^7-224*x^8-233*x^9-162*x^10- 147*x^11-58*x^12-3*x^13-4*x^14-x^15)/((1-x)*(1+x+x^2-x^3)^3*(1-3*x-x^2-x^3)^3) )); // G. C. Greubel, Nov 22 2021

(Sage)

@CachedFunction

def T(n): # A000073

    if (n<2): return 0

    elif (n==2): return 1

    else: return T(n-1) +T(n-2) +T(n-3)

def A337286(n): return sum( j^2*T(j)^2 for j in (0..n) )

[A337286(n) for n in (0..40)] # G. C. Greubel, Nov 22 2021

CROSSREFS

Cf. A000073, A085697, A337282, A337283, A337284, A337285.

Sequence in context: A012261 A012075 A197942 * A140417 A301396 A221512

Adjacent sequences:  A337283 A337284 A337285 * A337287 A337288 A337289

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Sep 12 2020

STATUS

approved

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Last modified September 24 18:11 EDT 2022. Contains 356949 sequences. (Running on oeis4.)