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 A050441 Partial sums of A051865. 4
 0, 1, 14, 50, 120, 235, 406, 644, 960, 1365, 1870, 2486, 3224, 4095, 5110, 6280, 7616, 9129, 10830, 12730, 14840, 17171, 19734, 22540, 25600, 28925, 32526, 36414, 40600, 45095, 49910, 55056, 60544, 66385, 72590, 79170, 86136, 93499, 101270 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS This sequence is related to A180223 by 2*a(n) = n*A180223(n) - Sum_{i=0..n-1} A180223(i). Also, 13-gonal (or tridecagonal) pyramidal numbers. - Bruno Berselli, Dec 14 2010 REFERENCES A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 189-196. E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 93. LINKS Bruno Berselli, Table of n, a(n) for n = 0..1000 B. Berselli, A description of the recursive method in Comments lines: website Matem@ticamente (in Italian), 2008. Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA a(n) = n*(n+1)*(11*n-8)/6. G.f.: x*(1+10*x)/(1-x)^4. - Bruno Berselli, Aug 19 2010 a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Bruno Berselli, Aug 19 2010 a(n) = Sum_{i=0..n-1} (n-i)*(11*i+1), with a(0)=0. - Bruno Berselli, Feb 10 2014 EXAMPLE After 0, the sequence is provided by the row sums of the triangle (see above, fourth formula):   1;   2, 12;   3, 24, 23;   4, 36, 46, 34;   5, 48, 69, 68, 45; ... - Vincenzo Librandi, Feb 12 2014 MAPLE seq(n*(n+1)*(11*n-8)/6, n=0..40); # G. C. Greubel, Aug 30 2019 MATHEMATICA Accumulate[Table[n (11n-9)/2, {n, 0, 40}]] (* or *) LinearRecurrence[ {4, -6, 4, -1}, {0, 1, 14, 50}, 40] (* Harvey P. Dale, Nov 14 2011 *) CoefficientList[Series[x (1 + 10 x)/(1 - x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Feb 12 2014 *) PROG (MAGMA) I:=[0, 1, 14, 50]; [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, Feb 12 2014 (PARI) a(n)=n*(n+1)*(11*n-8)/6 \\ Charles R Greathouse IV, Oct 07 2015 (Sage) [n*(n+1)*(11*n-8)/6 for n in (0..40)] # G. C. Greubel, Aug 30 2019 (GAP) List([0..40], n-> n*(n+1)*(11*n-8)/6); # G. C. Greubel, Aug 30 2019 CROSSREFS Cf. A051865, A180223. Cf. similar sequences listed in A237616. Sequence in context: A005914 A009960 A009928 * A225921 A205354 A281699 Adjacent sequences:  A050438 A050439 A050440 * A050442 A050443 A050444 KEYWORD nonn,easy,nice AUTHOR Barry E. Williams, Dec 23 1999 STATUS approved

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Last modified February 23 07:09 EST 2020. Contains 332159 sequences. (Running on oeis4.)