The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A231306 Recurrence a(n) = a(n-2) + n^M for M=7, starting with a(0)=0, a(1)=1. 7
0, 1, 128, 2188, 16512, 80313, 296448, 903856, 2393600, 5686825, 12393600, 25173996, 48225408, 87922513, 153638912, 258781888, 422074368, 669120561, 1034294400, 1562992300, 2314294400, 3364080841, 4808652288, 6768906288, 9395123712, 12872421913, 17426933888 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Stanislav Sýkora, Magnetic Resonance on OEIS, Stan's NMR Blog (Dec 31, 2014), Retrieved Nov 12, 2019.
Index entries for linear recurrences with constant coefficients, signature (8,-27,48,-42,0,42,-48,27,-8,1).
FORMULA
a(n) = Sum_{k=0..floor(n/2)} (n-2k)^7.
From Colin Barker, Dec 22 2015: (Start)
a(n) = 1/96*(6*n^8+48*n^7+112*n^6-224*n^4+256*n^2+51*((-1)^n-1)).
G.f.: x*(1+120*x+1191*x^2+2416*x^3+1191*x^4+120*x^5+x^6) / ((1-x)^9*(1+x)).
(End)
EXAMPLE
a(5) = 5^7 + 3^7 + 1^7 = 80313.
MATHEMATICA
Table[SeriesCoefficient[x (1 + 120 x + 1191 x^2 + 2416 x^3 + 1191 x^4 + 120 x^5 + x^6)/((1 - x)^9 (1 + x)), {x, 0, n}], {n, 0, 26}] (* Michael De Vlieger, Dec 22 2015 *)
LinearRecurrence[{8, -27, 48, -42, 0, 42, -48, 27, -8, 1}, {0, 1, 128, 2188, 16512, 80313, 296448, 903856, 2393600, 5686825}, 30] (* Vincenzo Librandi, Dec 23 2015 *)
nxt[{n_, a_, b_}]:={n+1, b, a+(n+1)^7}; NestList[nxt, {1, 0, 1}, 30][[All, 2]] (* Harvey P. Dale, Jun 16 2022 *)
PROG
(PARI) nmax=100; a = vector(nmax); a[2]=1; for(i=3, #a, a[i]=a[i-2]+(i-1)^7); print(a);
(PARI) concat(0, Vec(x*(1+120*x+1191*x^2+2416*x^3+1191*x^4+120*x^5+x^6)/((1-x)^9*(1+x)) + O(x^50))) \\ Colin Barker, Dec 22 2015
CROSSREFS
Cf. A001477 (M=1), A000292 (M=2), A105636 (M=3), A231303 (M=4), A231304 (M=5), A231305 (M=6), A231307 (M=8), A231308 (M=9), A231309 (M=10).
Sequence in context: A092759 A056574 A096961 * A236209 A283548 A297687
KEYWORD
nonn,easy
AUTHOR
Stanislav Sykora, Nov 07 2013
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 12 23:30 EDT 2024. Contains 373362 sequences. (Running on oeis4.)