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A101103 Partial sums of A101104. First differences of A005914. 6
1, 13, 36, 60, 84, 108, 132, 156, 180, 204, 228, 252, 276, 300, 324, 348, 372, 396, 420, 444, 468, 492, 516, 540, 564, 588, 612, 636, 660, 684, 708, 732, 756, 780, 804, 828, 852, 876, 900, 924, 948, 972, 996, 1020, 1044, 1068, 1092, 1116, 1140, 1164, 1188, 1212, 1236, 1260 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For more information, cross-references etc., see A101104.

For n >= 3, a(n) is equal to the number of functions f:{1,2,3,4}->{1,2,...,n} such that Im(f) contains 3 fixed elements. - Aleksandar M. Janjic and Milan Janjic, Mar 08 2007

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

C. J. Pita Ruiz V., Some Number Arrays Related to Pascal and Lucas Triangles, J. Int. Seq. 16 (2013) #13.5.7.

Index entries for linear recurrences with constant coefficients, signature (2, -1).

FORMULA

a(n) = 2*a(n-1) - a(n-2), n > 4.

G.f.: x*(1+x)*(1 + 10*x + x^2)/(1-x)^2.

a(n) = 24*n - 36, n >= 3.

a(n) = Sum_{j=0..n} (-1)^j*binomial(3, j)*(n - j)^4. [Indices shifted, Nov 01 2010]

a(n) = Sum_{i=1..4} A008292(4,i)*binomial(n-i+1,1). [Indices shifted, Nov 01 2010]

MAPLE

seq(coeff(series(x*(1+x)*(1+10*x+x^2)/(1-x)^2, x, n+1), x, n), n = 1 .. 60); # Muniru A Asiru, Dec 02 2018

MATHEMATICA

MagicNKZ=Sum[(-1)^j*Binomial[n+1-z, j]*(k-j+1)^n, {j, 0, k+1}]; Table[MagicNKZ, {n, 4, 4}, {z, 2, 2}, {k, 0, 34}] OR SeriesAtLevelR = Sum[Eulerian[n, i - 1]*Binomial[n + x - i + r, n + r], {i, 1, n}]; Table[SeriesAtLevelR, {n, 4, 4}, {r, -3, -3}, {x, 3, 35}]

Join[{1, 13}, LinearRecurrence[{2, -1}, {36, 60}, 33]] (* Ray Chandler, Sep 23 2015 *)

PROG

(PARI) my(x='x+O('x^60)); Vec(x*(1+x)*(1+10*x+x^2)/(1-x)^2) \\ G. C. Greubel, Dec 01 2018

(MAGMA) I:=[36, 60]; [1, 13] cat [n le 2 select I[n] else 2*Self(n-1) - Self(n-2): n in [1..30]]; // G. C. Greubel, Dec 01 2018

(Sage) s=(x*(1+x)*(1+10*x+x^2)/(1-x)^2).series(x, 30); s.coefficients(x, sparse=False) # G. C. Greubel, Dec 01 2018

(GAP) Concatenation([1, 13], List([3..60], n->24*n-36)); # Muniru A Asiru, Dec 02 2018

CROSSREFS

Cf. A073762.

Sequence in context: A272108 A034119 A054285 * A051865 A081928 A034129

Adjacent sequences:  A101100 A101101 A101102 * A101104 A101105 A101106

KEYWORD

easy,nonn

AUTHOR

Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 15 2004

EXTENSIONS

Removed redundant information already in A101104. Reduced formulas by expansion of constants - R. J. Mathar, Nov 01 2010

STATUS

approved

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Last modified December 15 20:00 EST 2019. Contains 330000 sequences. (Running on oeis4.)