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A050409 Truncated square pyramid numbers: a(n) = Sum_{k=n..2*n} k^2. 9
0, 5, 29, 86, 190, 355, 595, 924, 1356, 1905, 2585, 3410, 4394, 5551, 6895, 8440, 10200, 12189, 14421, 16910, 19670, 22715, 26059, 29716, 33700, 38025, 42705, 47754, 53186, 59015, 65255, 71920, 79024, 86581, 94605, 103110, 112110, 121619 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

M. Janjic and B. Petkovic, A Counting Function, arXiv preprint arXiv:1301.4550 [math.CO], 2013. - From N. J. A. Sloane, Feb 13 2013

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

a(n) = n*(n+1)*(14*n+1)/6.

a(n) = A132121(n,4) for n>3. - Reinhard Zumkeller, Aug 12 2007

G.f.: x*(5+9*x)/(1-x)^4. a(n) = A129371(2*n). - Bruno Berselli, Feb 11 2011

a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). - Vincenzo Librandi, Jun 22 2012

MAPLE

seq(add((n+k)^2, k=0..n), n=0..37); # Zerinvary Lajos, Dec 01 2006

MATHEMATICA

LinearRecurrence[{4, -6, 4, -1}, {0, 5, 29, 86}, 40] (* Vincenzo Librandi, Jun 22 2012

PROG

(MAGMA) [&+[k^2: k in [n..2*n]]: n in [0..37]]; // Bruno Berselli, Feb 11 2011

(PARI) a(n)=sum(k=n, n+n, k^2)

(MAGMA) I:=[0, 5, 29, 86]; [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, Jun 22 2012

CROSSREFS

Cf. A000330, A033994, A129371, A132112, A132121, A132124.

Cf. A225144. [Bruno Berselli, Jun 06 2013]

Sequence in context: A154412 A236075 A272650 * A111937 A215850 A190585

Adjacent sequences:  A050406 A050407 A050408 * A050410 A050411 A050412

KEYWORD

easy,nice,nonn

AUTHOR

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 22 1999

STATUS

approved

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Last modified July 21 04:27 EDT 2017. Contains 289632 sequences.