0,6

"In this work, we introduce a symmetric algorithm based on the recurrence relation a_{n}^{k}=a_{n-1}^{k}+a_{n}^{k-1}. We point out that this algorithm can be applied to hyperharmonic, ordinary and incomplete Fibonacci and Lucas numbers. An explicit formulae for hyperharmonic numbers, and generating functions of the Fibonacci- and Lucas numbers are obtained.

We also define "hyperfibonacci numbers", "hyperlucas numbers". Using these new concepts, some relations between ordinary and incomplete Fibonacci- and Lucas numbers are investigated." [Dil and Mezo]

Ayhan Dil, Istvan Mezo, A Symmetric Algorithm for Hyperharmonic and Fibonacci Numbers

Eric W. Weisstein, Steenrod Algebra,

a(k,n) = Apply partial sum operator k times to Lucas numbers A000204.

The array L(n)^{k} begins:

....|n=0|n=1|.n=2|.n=3|.n=4.|.n=5.|..n=6.|.n=7..|..n=8..|..n=9..|.n=10..|.in.OEIS

k=0..|.0.|.1.|..3.|..4.|...7.|..11.|...18.|...29.|....47.|....76.|...123.|.A000204

k=1..|.0.|.1.|..4.|..8.|..15.|..26.|...44.|...73.|...120.|...196.|...319.|.A027961

k=2..|.0.|.1.|..5.|.13.|..28.|..54.|...98.|..171.|...291.|...487.|...806.|.A023537

k=3..|.0.|.1.|..6.|.19.|..47.|.101.|..199.|..370.|...661.|..1148.|..1954.|.A027963

k=4..|.0.|.1.|..7.|.26.|..73.|.174.|..373.|..743.|..1404.|..2552.|..4506.|.A027964

k=5..|.0.|.1.|..8.|.34.|.107.|.281.|..654.|.1397.|..2801.|..5353.|..9859.|.A053298

k=6..|.0.|.1.|..9.|.43.|.150.|.431.|.1085.|.2482.|..5283.|.10636.|.20495.|.new

k=7..|.0.|.1.|.10.|.53.|.203.|.634.|.1719.|.4201.|..9484.|.20120.|.40615.|.new

k=8..|.0.|.1.|.11.|.64.|.267.|.901.|.2620.|.6821.|.16305.|.36425.|.77040.|.new

k=9..|.0.|.1.|.12.|.76.|.343.|1244.|.3864.|10685.|.26990.|.63415.|140455.|.new

Cf. A000204, A027961, A023537, A027963, A027964, A053298, A123736.

Adjacent sequences: A137173 A137174 A137175 this_sequence A137177 A137178 A137179

Sequence in context: A106356 A091613 A039727 this_sequence A143949 A124323 A106683

easy,nonn,tabl

Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 04 2008