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A048397
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Sum of consecutive non-fourth-powers.
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3
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0, 119, 3104, 29319, 162104, 643535, 2040744, 5502959, 13129424, 28468359, 57167120, 107793719, 192849864, 329995679, 543506264, 865980255, 1340320544, 2022007319, 2981683584, 4308073319, 6111252440, 8526292719, 11717298824
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OFFSET
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0,2
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COMMENTS
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Relationship with tetrahedral numbers: a(4) = (first term + last term)*(6*Tetra_n + n^3) = (82+255)*(6*10+27) = (337)*(87) = 29319.
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LINKS
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FORMULA
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a(n) = 4*n^7 + 14*n^6 + 28*n^5 + 34*n^4 + 26*n^3 + 11*n^2 + 2*n.
G.f.: (119*x +2152*x^2 +7819*x^3 +7800*x^4 +2141*x^5 +128*x^6 +x^7)/(x-1)^8. - Harvey P. Dale, Apr 23 2011
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EXAMPLE
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Between 3^4 and 4^4 we have 82+83+...+254+255 which is 29319 or a(4).
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MAPLE
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MATHEMATICA
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Table[Total[Range[n^4+1, (n+1)^4-1]], {n, 0, 40}] (* or *) Table[4n^7+ 14n^6+28n^5+34n^4+26n^3+11n^2+2n, {n, 0, 40}] (* Harvey P. Dale, Apr 23 2011 *)
LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {0, 119, 3104, 29319, 162104, 643535, 2040744, 5502959}, 40] (* Harvey P. Dale, Jul 31 2021 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,nice,easy
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AUTHOR
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STATUS
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approved
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