This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A051895 Partial sums of second pentagonal numbers with even index (A049453). 4
 0, 7, 33, 90, 190, 345, 567, 868, 1260, 1755, 2365, 3102, 3978, 5005, 6195, 7560, 9112, 10863, 12825, 15010, 17430, 20097, 23023, 26220, 29700, 33475, 37557, 41958, 46690, 51765, 57195, 62992, 69168, 75735, 82705, 90090, 97902, 106153, 114855, 124020, 133660 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS For A049453(n+1), the corresponding formula would be a(n)=(n+1)*(6*n+7) and its partial sums would be given by a(n)=(n+1)*(n+2)*(4*n+7)/2. REFERENCES A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA a(n) = n*(n+1)*(4*n+3)/2. G.f.: x*(7+5*x)/(1-x)^4. - Colin Barker, Jan 12 2012 a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). - Vincenzo Librandi, Apr 27 2012 a(n) = A002492(n) + A016061(n). - J. M. Bergot, Apr 20 2018 MATHEMATICA Table[(n(4n-1)(n-1))/2, {n, 40}]  (* Harvey P. Dale, Mar 11 2011 *) CoefficientList[Series[x*(7+5*x)/(1-x)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Apr 27 2012 *) PROG (MAGMA) I:=[0, 7, 33, 90]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Apr 27 2012 (PARI) a(n) = n*(n+1)*(4*n+3)/2; \\ Altug Alkan, Apr 20 2018 CROSSREFS Cf. A002492, A016061, A017605, A049453. Sequence in context: A153286 A060745 A275163 * A168574 A212106 A131211 Adjacent sequences:  A051892 A051893 A051894 * A051896 A051897 A051898 KEYWORD nonn,easy AUTHOR Barry E. Williams, Dec 17 1999 STATUS approved

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

Last modified April 22 04:04 EDT 2019. Contains 322329 sequences. (Running on oeis4.)