A178617 a(n) = n^4 - (n+1)^3.
-1, -7, -11, 17, 131, 409, 953, 1889, 3367, 5561, 8669, 12913, 18539, 25817, 35041, 46529, 60623, 77689, 98117, 122321, 150739, 183833, 222089, 266017, 316151, 373049, 437293, 509489, 590267, 680281, 780209, 890753, 1012639, 1146617
Offset: 0
Examples
-7 is an element since 1^4 - 2^3 = 1 - 8 = -7, -11 is an element since 2^4 - 3^3 = 16 - 27 = -11.
Links
- G. C. Greubel, Table of n, a(n) for n = 0..5000
- Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).
Programs
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GAP
List([0..40], n -> n^4-(n+1)^3); # G. C. Greubel, Jan 29 2019
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Magma
[n^4-(n+1)^3: n in [0..40]]; // G. C. Greubel, Jan 29 2019
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Mathematica
Table[n^4-(n+1)^3,{n,0,40}] LinearRecurrence[{5,-10,10,-5,1},{-1,-7,-11,17,131},40] (* Harvey P. Dale, Jan 30 2013 *) -
PARI
vector(40, n, n--; n^4-(n+1)^3) \\ G. C. Greubel, Jan 29 2019
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Sage
[n^4-(n+1)^3 for n in (0..40)] # G. C. Greubel, Jan 29 2019
Formula
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5), where a(0)=-1, a(1)=-7, a(2)=-11, a(3)=17, a(4)=131. - Harvey P. Dale, Jan 30 2013
From G. C. Greubel, Jan 29 2019: (Start)
G.f.: (-1 - 2*x + 14*x^2 + 12*x^3 + x^4)/(1-x)^5.
E.g.f.: (-1 - 6*x + x^2 + 5*x^3 + x^4)*exp(x). (End)