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A048395 Sum of consecutive nonsquares. 12
0, 5, 26, 75, 164, 305, 510, 791, 1160, 1629, 2210, 2915, 3756, 4745, 5894, 7215, 8720, 10421, 12330, 14459, 16820, 19425, 22286, 25415, 28824, 32525, 36530, 40851, 45500, 50489, 55830, 61535, 67616, 74085, 80954, 88235, 95940, 104081 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Relationship with natural numbers: a(4) = (first term + last term)*n = (10+15)*3 = (25)*3 = 75; a(5) = (17+24)*4 = (41)4 = 164; ...

Also (X*Y*Z)/(X+Y+Z) of primitive Pythagorean triples (X,Y,Z=Y+1) as described in A046092 and A001844. - Lambert Herrgesell (zero815(AT)googlemail.com), Dec 13 2005

a(n) = A199771(2*n) for n > 0. - Reinhard Zumkeller, Nov 23 2011

Partial sums of A201279. - J. M. Bergot, Jun 22 2013

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for sequences related to sums of squares

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

FORMULA

a(n) = 2*n^3 + 2*n^2 + n.

a(n) = Sum_{j=0..n} ((n+j+2)^2 - j^2 + 1). - Zerinvary Lajos, Sep 13 2006

O.g.f.: x(x+5)(1+x)/(1-x)^4. - R. J. Mathar, Jun 12 2008

a(0)=0, a(1)=5, a(2)=26, a(3)=75, a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Harvey P. Dale, Nov 01 2013

EXAMPLE

Between 3^2 and 4^2 we have 10+11+12+13+14+15 which is 75 or a(4).

MATHEMATICA

Table[n(1+2*n(1+n)), {n, 0, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 5, 26, 75}, 40] (* Harvey P. Dale, Nov 01 2013 *)

PROG

(PARI) v0=[1, 0, 1]; M=[1, 2, 2; -2, -1, -2; 2, 2, 3];

g(v)=v[1]*v[2]*v[3]/(v[1]+v[2]+v[3]);

a(n)=g(v0*M^n);

for(i=0, 50, print1(a(i), ", ")) \\ Lambert Herrgesell (zero815(AT)googlemail.com), Dec 13 2005

(Haskell)

a048395 0 = 0

a048395 n = a199771 (2 * n)  -- Reinhard Zumkeller, Oct 26 2015

CROSSREFS

Cf. A048396, A048397, A046092, A001844.

Cf. A001844, A046092, A086849, A199771, A201279.

Sequence in context: A273833 A273849 A273781 * A081886 A081530 A254831

Adjacent sequences:  A048392 A048393 A048394 * A048396 A048397 A048398

KEYWORD

nonn,nice,easy

AUTHOR

Patrick De Geest, Mar 15 1999

STATUS

approved

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Last modified August 21 21:17 EDT 2017. Contains 290907 sequences.