A000584 -id:A000584 - cp's OEIS frontend

A006414 Number of nonseparable toroidal tree-rooted maps with n + 2 edges and n + 1 vertices.

1, 9, 40, 125, 315, 686, 1344, 2430, 4125, 6655, 10296, 15379, 22295, 31500, 43520, 58956, 78489, 102885, 133000, 169785, 214291, 267674, 331200, 406250, 494325, 597051, 716184, 853615, 1011375, 1191640, 1396736, 1629144, 1891505, 2186625, 2517480, 2887221

Offset: 0

N. J. A. Sloane

The number of faces is 1.
a(n) = K(Oa(2,3,n)), Kekulé numbers of certain benzenoid structures (see the Cyvin - Gutman reference).
Sequence of partial sums of A006322. - L. Edson Jeffery, Dec 13 2011
The sequence b(n) = a(n-2) with a(-1) = 0, for n >= 1, is b(n) = n^3*(n^2 - 1)/4!. It is obtained by comparing the result for the powers n^5 from Worpitzky's identity (see a formula in A000584) with the result obtained from the counting of degrees of freedom for the decomposition of a rank 5 tensor in n dimensions via the standard Young tableaux version with 5 boxes corresponding to the seven partitions of 5. The difference of the two versions gives: 10*(binomial(n+3, 5) + 3*binomial(n+2, 5) + binomial(n+1, 5)) = 5*n*(binomial(n+2, 4) + binomial(n+1, 4)) = 10*b(n). See the formula for a(n) below. - Wolfdieter Lang, Jul 18 2019

S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988, p. 105, eq. (ii), and p. 186.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
T. R. S. Walsh and A. B. Lehman, Counting rooted maps by genus. III: Nonseparable maps, J. Combinatorial Theory Ser. B, Vol. 18, No. 3 (1975), pp. 222-259.
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Differences of A006542 (C(n, 3)*C(n-1, 3)/4).

Cf. A004068, A005891, A006322, A006415, A006434, A006441, A133754, A143945.

List([0..40], n-> (n+2)^2*Binomial(n+3,3)/4 ); G. C. Greubel, Sep 02 2019

[(n+1)*(n+2)^3*(n+3)/24: n in [0..40]]; // Wesley Ivan Hurt, May 10 2014

seq((n+2)^2*binomial(n+3,3)/4, n=0..40); # G. C. Greubel, Sep 02 2019

Table[(n + 1)*(n + 2)^3*(n + 3)/24, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Apr 18 2011 *)

a(n) = (n+1)*(n+2)^3*(n+3)/24; \\ Michel Marcus, Jul 09 2017

[(n+2)^2*binomial(n+3,3)/4 for n in (0..40)] # G. C. Greubel, Sep 02 2019

a(n) = (n+1)*(n+2)^3*(n+3)/24. - N. J. A. Sloane, Apr 02 2004
a(n) = (n+2)^3*((n+2)^2 - 1)/24. - Paul Richards, Mar 04 2007
G.f.: (1 + 3*x + x^2)/(1-x)^6. - Colin Barker, Feb 21 2012
a(n) = (Sum_{k=0..n+1} k*(n+1)*((n+1)^2 - k^2))/6 for n > 0, which is the sum of all areas of Pythagorean triangles with arms 2*k*(n+1) and (n+1)^2 - k^2 with hypotenuse k^2 + (n+1)^2. - J. M. Bergot, May 12 2014
a(n) = A143945(n+2)/8. - J. M. Bergot, Jun 14 2014
Sum_{n>=0} 1/a(n) = 30 - 24*zeta(3). - Jaume Oliver Lafont, Jul 09 2017
a(n) = binomial(n+5, 5) + 3*binomial(n+4, 5) + binomial(n+3, 5) = ((n+2)/2)*(binomial(n+4, 4) + binomial(n+3, 4)), for n >= 0. See a comment above on the sequence b(n) = a(n-2) = n^3*(n^2 - 1)/4!. - Wolfdieter Lang, Jul 19 2019
E.g.f.: (24 + 192*x + 276*x^2 + 124*x^3 + 20*x^4 + x^5)*exp(x)/4!. - G. C. Greubel, Sep 02 2019
Sum_{n>=0} (-1)^n/a(n) = 18*zeta(3) + 48*log(2) - 54. - Amiram Eldar, Jan 09 2022

More terms from Robert Newstedt (Patternfinder(AT)webtv.net)

Name clarified by Andrew Howroyd, Apr 05 2021

A010801 13th powers: a(n) = n^13.

Original entry on oeis.org

0, 1, 8192, 1594323, 67108864, 1220703125, 13060694016, 96889010407, 549755813888, 2541865828329, 10000000000000, 34522712143931, 106993205379072, 302875106592253, 793714773254144, 1946195068359375, 4503599627370496, 9904578032905937, 20822964865671168

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).

Cf. A000290 (squares), A000578 (cubes), A000583 (4th powers), A000584 (5th powers), A008455 (11th powers), A013671 (zeta(11)).

[n^13: n in [0..15]]; // Vincenzo Librandi, Jun 19 2011

A010801 := n -> n^13; \\ M. F. Hasler, Jul 03 2025

Range[0,30]^13 (* Vladimir Joseph Stephan Orlovsky, Mar 14 2011 *)

A010801(n)=n^13 \\ Charles R Greathouse IV, Oct 07 2015

A010801 = lambda n: n**13 # M. F. Hasler, Jul 03 2025

a(n) mod 10 = n mod 10. - Reinhard Zumkeller, Dec 06 2004
Totally multiplicative with a(p) = p^13 for primes p. Multiplicative with a(p^e) = p^(13*e). - Jaroslav Krizek, Nov 01 2009
G.f.: x*(x^12 + 8178*x^11 + 1479726*x^10 + 45533450*x^9 + 423281535*x^8 + 1505621508*x^7 + 2275172004*x^6 + 1505621508*x^5 + 423281535*x^4 + 45533450*x^3 + 1479726*x^2 + 8178*x + 1) / (x - 1)^14. - Colin Barker, Sep 25 2014
From Amiram Eldar, Oct 08 2020: (Start)
Sum_{n>=1} 1/a(n) = zeta(13) (A013671).
Sum_{n>=1} (-1)^(n+1)/a(n) = 4095*zeta(13)/4096. (End)

A206852 Numbers N such that N/2 is a square, N/3 is a cube, and N/5 is a fifth power.

Original entry on oeis.org

30233088000000, 32462531054272512000000, 6224724715037147546112000000, 34856377305871210027941888000000, 28156757354736328125000000000000000, 6683747269421867033919422988288000000, 681433858470444619689081338982912000000

Offset: 1

M. F. Hasler, Feb 15 2012

The terms must be of the form N = 2^a*3^b*5^c*m^(2*3*5) where gcd(m, 2*3*5) = 1 and a-1, b-1 and c-1 must be a multiple of 2, 3 and 5, respectively, and a, b, c must be a multiple of the two other prime factors, respectively. This gives (a, b, c) == (3*5, 2*5, 2*3) [mod 2*3*5], whence N = 2^15*3^10*5^6*n^30. - M. F. Hasler, Jul 22 2022

Georg Fischer, Table of n, a(n) for n = 1..1000
Shyam Sunder Gupta, Do you know, as of Feb 15 2012.
Michael Penn, a sunny number puzzle!, YouTube video, 2021.
Index entries for linear recurrences with constant coefficients, signature (31, -465, 4495, -31465, 169911, -736281, 2629575, -7888725, 20160075, -44352165, 84672315, -141120525, 206253075, -265182525, 300540195, -300540195, 265182525, -206253075, 141120525, -84672315, 44352165, -20160075, 7888725, -2629575, 736281, -169911, 31465, -4495, 465, -31, 1).

Cf. A000290 (squares), A000578 (cubes), A000584 (5th powers), A122971 (30th powers).

Table[30233088000000 * n^30, {n,1,1000}] (* Georg Fischer, Feb 07 2021 *)

{is_A206852(n)=(n=divrem(n,3^10*5^6<<15))[2]==0 && ispower(n[1],30)} \\ replacing obsolete PARI code from 2012. - M. F. Hasler, Jul 22 2022

a(n)=30233088000000*n^30 \\ Charles R Greathouse IV, Apr 25 2012

def A206852(n): return 30233088000000*n**30 # M. F. Hasler, Jul 24 2022

def is_A206852(n):
    for p in (2, 3, 5):
        for e in range(n):
            if n % p: break
            n //= p
        if e % 30 != 30//p: return False
    return is_A122971(n) # M. F. Hasler, Jul 24 2022

a(n) = 30233088000000 * n^30 = 2^15 * 3^10 * 5^6 * n^30. - Charles R Greathouse IV, Apr 25 2012

A244003 A(n,k) = k^Fibonacci(n); square array A(n,k), n>=0, k>=0, read by antidiagonals.

Original entry on oeis.org

1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 2, 1, 0, 1, 4, 3, 4, 1, 0, 1, 5, 4, 9, 8, 1, 0, 1, 6, 5, 16, 27, 32, 1, 0, 1, 7, 6, 25, 64, 243, 256, 1, 0, 1, 8, 7, 36, 125, 1024, 6561, 8192, 1, 0, 1, 9, 8, 49, 216, 3125, 65536, 1594323, 2097152, 1, 0

Offset: 0

Alois P. Heinz, Jun 17 2014

			Square array A(n,k) begins:
  1, 1,   1,    1,     1,      1,       1, ...
  0, 1,   2,    3,     4,      5,       6, ...
  0, 1,   2,    3,     4,      5,       6, ...
  0, 1,   4,    9,    16,     25,      36, ...
  0, 1,   8,   27,    64,    125,     216, ...
  0, 1,  32,  243,  1024,   3125,    7776, ...
  0, 1, 256, 6561, 65536, 390625, 1679616, ...

Alois P. Heinz, Antidiagonals n = 0..20, flattened

Columns k=0-10 give: A000007, A000012, A000301, A010098, A010099, A214706, A215270, A214887, A215271, A215272, A010100.
Rows n=0, 1+2, 3-8 give: A000012, A001477, A000290, A000578, A000584, A001016, A010801, A010809.
Main diagonal gives: A152915.
Cf. A000045, A103323.

A:= (n, k)-> k^(<<1|1>, <1|0>>^n)[1, 2]:
seq(seq(A(n, d-n), n=0..d), d=0..12);

A[0, 0] = 1; A[n_, k_] := k^Fibonacci[n]; Table[A[n-k, k], {n, 0, 12}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Nov 11 2015 *)

A(n,k) = k^A000045(n).

A(0,k) = 1, A(1,k) = k, A(n,k) = A(n-1,k) * A(n-2,k) for n>=2.

A008382 a(n) = floor(n/5)floor((n+1)/5)floor((n+2)/5)floor((n+3)/5)floor((n+4)/5).

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 2, 4, 8, 16, 32, 48, 72, 108, 162, 243, 324, 432, 576, 768, 1024, 1280, 1600, 2000, 2500, 3125, 3750, 4500, 5400, 6480, 7776, 9072, 10584, 12348, 14406, 16807, 19208, 21952, 25088, 28672, 32768, 36864, 41472, 46656, 52488, 59049, 65610, 72900, 81000

Offset: 0

N. J. A. Sloane

nonn

For n >= 5, a(n) is the maximal product of 5 positive integers with sum n. - Wesley Ivan Hurt, Jun 29 2022

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,4,-8,4,0,0,-6,12,-6,0,0,4,-8,4,0,0,-1,2,-1).

Maximal product of k positive integers with sum n, for k = 2..10: A002620 (k=2), A006501 (k=3), A008233 (k=4), this sequence (k=5), A008881 (k=6), A009641 (k=7), A009694 (k=8), A009714 (k=9), A354600 (k=10).

Cf. A000584, A013663.

CoefficientList[Series[x^5*(x^10 - 2*x^9 + 4*x^8 - 4*x^7 + 8*x^6 - 8*x^5 + 8*x^4 - 4*x^3 + 4*x^2 - 2*x + 1)*(1 + x)^2/((x^4 + x^3 + x^2 + x + 1)^4*(x - 1)^6), {x, 0, 60}], x] (* Wesley Ivan Hurt, Jun 29 2022 *)

A008382(n):=floor(n/5)*floor((n+1)/5)*floor((n+2)/5)*floor((n+3)/5)*floor((n+4)/5)$
makelist(A008382(n),n,0,30); /* Martin Ettl, Oct 26 2012 */

From R. J. Mathar, May 08 2013: (Start)
a(n) = +2*a(n-1) -a(n-2) +4*a(n-5) -8*a(n-6) +4*a(n-7) -6*a(n-10) +12*a(n-11) -6*a(n-12) +4*a(n-15) -8*a(n-16) +4*a(n-17) -a(n-20) +2*a(n-21) -a(n-22).
G.f.: x^5 *(x^10 -2*x^9 +4*x^8 -4*x^7 +8*x^6 -8*x^5 +8*x^4 -4*x^3 +4*x^2 -2*x+1) *(1+x)^2 / ( (x^4+x^3+x^2+x+1)^4 *(x-1)^6 ). (End)
a(5*m) = m^5 (A000584). - Bernard Schott, Sep 21 2022
Sum_{n>=5} 1/a(n) = 1 + zeta(5). - Amiram Eldar, Jan 10 2023

A017501 a(n) = (11*n + 9)^5.

Original entry on oeis.org

59049, 3200000, 28629151, 130691232, 418195493, 1073741824, 2373046875, 4704270176, 8587340257, 14693280768, 23863536599, 37129300000, 55730836701, 81136812032, 115063617043, 159494694624

Offset: 0

N. J. A. Sloane

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Powers of the form (11*n+9)^m: A017497 (m=1), A017498 (m=2), A017499 (m=3), A017500 (m=4), this sequence (m=5), A017502 (m=6), A017503 (m=7), A017504 (m=8), A017505 (m=9), A017506 (m=10), A017607 (m=11), A017508 (m=12).

Subsequence of A000584.

List([0..20], n-> (11*n+9)^5); # G. C. Greubel, Oct 28 2019

[(11*n+9)^5: n in [0..20]]; // G. C. Greubel, Oct 28 2019

seq((11*n+9)^5, n=0..20); # G. C. Greubel, Oct 28 2019

(11*Range[0,20]+9)^5 (* or *) LinearRecurrence[{6,-15,20,-15,6,-1}, {59049,3200000,28629151,130691232,418195493,1073741824},20] (* Harvey P. Dale, Jan 25 2013 *)

vector(21, n, (11*n-2)^5) \\ G. C. Greubel, Oct 28 2019

[(11*n+9)^5 for n in (0..20)] # G. C. Greubel, Oct 28 2019

a(0)=59049, a(1)=3200000, a(2)=28629151, a(3)=130691232, a(4)=418195493, a(5)=1073741824, a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6). - Harvey P. Dale, Jan 25 2013
G.f.: (59049 + 2845706*x + 10314886*x^2 + 5735346*x^3 + 371101*x^4 + 32*x^5) / (1-x)^6. - Harvey P. Dale, Jan 25 2013
E.g.f.: (59049 + 3140951*x + 11144100*x^2 + 9057455*x^3 + 2269355*x^4 + 161051*x^5)*exp(x). - G. C. Greubel, Oct 28 2019

A038993 Number of sublattices of index n in generic 6-dimensional lattice.

Original entry on oeis.org

1, 63, 364, 2667, 3906, 22932, 19608, 97155, 99463, 246078, 177156, 970788, 402234, 1235304, 1421784, 3309747, 1508598, 6266169, 2613660, 10417302, 7137312, 11160828, 6728904, 35364420, 12714681, 25340742, 25095280, 52294536, 21243690, 89572392, 29583456

Offset: 1

N. J. A. Sloane

Michael Baake, "Solution of the coincidence problem in dimensions d <= 4", in R. V. Moody, ed., Math. of Long-Range Aperiodic Order, Kluwer 1997, pp. 9-44.

Amiram Eldar, Table of n, a(n) for n = 1..10000
M. Baake and N. Neumarker, A Note on the Relation Between Fixed Point and Orbit Count Sequences, JIS 12 (2009) 09.4.4, Section 3.
Index entries for sequences related to sublattices.

Column 6 of A160870.

Cf. A001001, A038991, A038992, A038994, A038995, A038996, A038997, A038998, A038999.

f[p_, e_] := Product[(p^(e + k) - 1)/(p^k - 1), {k, 1, 5}]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Aug 29 2019 *)

f(Q, n) = Sum_{d|n} d*f(Q-1, d); here Q=6.
Multiplicative with a(p^e) = product (p^(e+k)-1)/(p^k-1), k=1..5.
Dirichlet g.f.: zeta(s)*zeta(s-1)*zeta(s-2)*zeta(s-3)*zeta(s-4)*zeta(s-5). Dirichlet convolution of A038992 with A000584. - R. J. Mathar, Mar 31 2011
Sum_{k=1..n} a(k) ~ c * n^6, where c = Pi^12*zeta(3)*zeta(5)/3061800 = 0.376266... . - Amiram Eldar, Oct 19 2022

Offset changed from 0 to 1 by R. J. Mathar, Mar 31 2011

More terms from Amiram Eldar, Aug 29 2019

A016781 a(n) = (3*n+1)^5.

Original entry on oeis.org

1, 1024, 16807, 100000, 371293, 1048576, 2476099, 5153632, 9765625, 17210368, 28629151, 45435424, 69343957, 102400000, 147008443, 205962976, 282475249, 380204032, 503284375, 656356768, 844596301, 1073741824, 1350125107, 1680700000, 2073071593, 2535525376

Offset: 0

N. J. A. Sloane

In general the e.g.f. of {(1 + 3*m)^n}{m>=0} is E(n,x) = exp(x)*Sum{m=0..n} A282629(n, m)*x^m, and the o.g.f. is G(n, x) = (Sum_{m=0..n} A225117(n, n-m)*x^m)/(1-x)^(n+1). - Wolfdieter Lang, Apr 02 2017

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Cf. A016777, A016778, A016779, A016780, A225117, A282629.

[(3*n+1)^5: n in [0..30]]; // Vincenzo Librandi, Sep 21 2011

(3Range[0,20]+1)^5 (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{1,1024,16807,100000,371293,1048576},30] (* Harvey P. Dale, May 13 2012 *)

A016781(n):=(3*n+1)^5$
makelist(A016781(n),n,0,20); /* Martin Ettl, Nov 12 2012 */

a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6). - Harvey P. Dale, May 13 2012
From Wolfdieter Lang, Apr 02 2017: (Start)
O.g.f.: (1+1018*x+10678*x^2+14498*x^3+2933*x^4+32*x^5)/(1-x)^6.
E.g.f: exp(x)*(1+1023*x+7380*x^2+8775*x^3+2835*x^4+243*x^5). (End)
a(n) = A000584(A016777(n)). - Michel Marcus, Apr 06 2017
Sum_{n>=0} 1/a(n) = 2*Pi^5/(3^6*sqrt(3)) + 121*zeta(5)/3^5. - Amiram Eldar, Mar 29 2022

A061167 a(n) = n^5 - n.

Original entry on oeis.org

0, 0, 30, 240, 1020, 3120, 7770, 16800, 32760, 59040, 99990, 161040, 248820, 371280, 537810, 759360, 1048560, 1419840, 1889550, 2476080, 3199980, 4084080, 5153610, 6436320, 7962600, 9765600, 11881350, 14348880, 17210340, 20511120, 24299970, 28629120

Offset: 0

Henry Bottomley, Apr 18 2001

(b^2+c^2)/(bc+1) is an integer if {b,c} are of the form {0,n}, {n,n^3}, {n^3,n^5-n}, {n^5-n,n^7-2n^3}, {n^7-2n^3,n^9-3n^5+n}, etc. for some n, in which case the division results in n^2. Cf. A052530.

Convolution of A033429 by A033581. - R. J. Mathar, Aug 19 2008

			a(2) = 32 - 2 = 30.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
D. Zagier, Problems posed at the St Andrews Colloquium, 1996
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Subsequence of A249674.

Cf. A000584, A024002, A033429, A033455, A033581, A052530.

[n^5-n: n in [0..40]]; // Vincenzo Librandi, May 02 2011

Table[n^5 - n, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2012 *)

a(n) = 30*A033455(n-1). [Corrected by Bernard Schott, Mar 16 2021]
a(n) = -n*A024002(n).
a(n) = A000584(n) - n.
O.g.f.: 30x^2(1+x)^2/(1-x)^6. - R. J. Mathar, Aug 19 2008
a(n) = n * (n-1) * (n+1) * (n^2+1). - Bernard Schott, Mar 16 2021
E.g.f.: exp(x)*x^2*(15 + 25*x + 10*x^2 + x^3). - Stefano Spezia, Dec 27 2021

A162622 Triangle read by rows in which row n lists n+1 terms, starting with n, such that the difference between successive terms is equal to n^4 - 1.

Original entry on oeis.org

0, 1, 1, 2, 17, 32, 3, 83, 163, 243, 4, 259, 514, 769, 1024, 5, 629, 1253, 1877, 2501, 3125, 6, 1301, 2596, 3891, 5186, 6481, 7776, 7, 2407, 4807, 7207, 9607, 12007, 14407, 16807, 8, 4103, 8198, 12293, 16388, 20483, 24578, 28673, 32768, 9, 6569, 13129

Offset: 0

Omar E. Pol, Jul 15 2009

Note that the last term of the n-th row is the 5th power of n, A000584(n).

See also the triangles of A162623 and A162624.

			Triangle begins:
  0;
  1,    1;
  2,   17,    32;
  3,   83,   163,   243;
  4,  259,   514,   769,  1024;
  5,  629,  1253,  1877,  2501,  3125;
  6, 1301,  2596,  3891,  5186,  6481,  7776;
  7, 2407,  4807,  7207,  9607, 12007, 14407, 16807;
  8, 4103,  8198, 12293, 16388, 20483, 24578, 28673, 32768;
  9, 6569, 13129, 19689, 26249, 32809, 39369, 45929, 52489, 59049; etc.

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Cf. A000583, A000584, A123865, A159797, A162609, A162610, A162611, A162612, A162613, A162614, A162615, A162616, A162623, A162624.

/* Triangle: */ [[n+k*(n^4-1): k in [0..n]]: n in [0..10]]; // Bruno Berselli, Dec 14 2012

A162622 := proc(n,k) n+k*(n^4-1) ; end proc: seq(seq( A162622(n,k),k=0..n),n=0..15) ; # R. J. Mathar, Feb 11 2010

Flatten[Table[NestList[#+n^4-1&,n,n],{n,0,9}]] (* Harvey P. Dale, Jun 23 2013 *)

Sum_{k=0..n} T(n,k) = n*(n+1)*(1+n^4)/2 (row sums). [R. J. Mathar, Jul 20 2009]

7th and later rows from R. J. Mathar, Feb 11 2010

cp's OEIS Frontend

A006414 Number of nonseparable toroidal tree-rooted maps with n + 2 edges and n + 1 vertices.

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A010801 13th powers: a(n) = n^13.

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A206852 Numbers N such that N/2 is a square, N/3 is a cube, and N/5 is a fifth power.

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A244003 A(n,k) = k^Fibonacci(n); square array A(n,k), n>=0, k>=0, read by antidiagonals.

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A008382 a(n) = floor(n/5)*floor((n+1)/5)*floor((n+2)/5)*floor((n+3)/5)*floor((n+4)/5).

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A017501 a(n) = (11*n + 9)^5.

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Sage

A008382 a(n) = floor(n/5)floor((n+1)/5)floor((n+2)/5)floor((n+3)/5)floor((n+4)/5).