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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 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 * A309451 A081886 A081530 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 October 17 22:05 EDT 2019. Contains 328134 sequences. (Running on oeis4.)