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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
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FORMULA
| 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 [From Harvey P. Dale, Apr 23 2011]
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EXAMPLE
| Between 3^4 and 4^4 we have 82+83+.. ..+254+255 which is 29319 or a(4).
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MATHEMATICA
| 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}] (* From Harvey P. Dale, Apr 23 2011 *)
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CROSSREFS
| Cf. A048395, A048396, A000292.
Sequence in context: A126563 A067134 A156930 * A020529 A163006 A069328
Adjacent sequences: A048394 A048395 A048396 * A048398 A048399 A048400
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KEYWORD
| nonn,nice
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AUTHOR
| Patrick De Geest (pdg(AT)worldofnumbers.com), Mar 15 1999.
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